Modeling 3D Ex-Filtration Process of a Soak-Away Rain Garden

This paper presents a three-dimensional (3D) model developed using COMSOL Multiphysics to understand the 3D ex-filtration process of a soak-away rain garden. With a design hyetograph of 3-month average rainfall intensities of Singapore, it is found that the average vertical ex-filtration rate that is obtained by dividing the average vertical ex-filtration (drained through bottom of the soak-away rain garden, averaged over the simulation period = 720 min, and expressed in m3) by the surface area of the soak-away rain garden and the simulation time step is almost constant regardless of increase in saturated hydraulic conductivity (K) of the in-situ soil and the surface area of the soak-away rain garden as a percentage of catchment area. However, as depth to groundwater table which is measured from bottom of the filter media increases, in between 0.5 m and 1 m of depth to groundwater table, the average vertical ex-filtration rate decreases significantly (by around 15 - 20 mm/hr) and the decrease is almost twice, compared with that between 1 m and 1.5 m of depth to groundwater table. Furthermore, this study shows that for a given K of in-situ, K of filter media, and depth to groundwater table, as the surface area of the soak-away rain garden increases, the horizontal flow coefficient which is defined as the ratio between total horizontal ex-filtration (drained through sides of the soak-away rain garden, summed over the simulation period, and expressed in m3) and total vertical ex-filtration (drained through bottom of the soak-away rain garden, summed over the simulation period, and expressed in m3) decreases. Moreover, for a given surface area of the soak-away rain garden, K of in-situ, and depth to groundwater table, the horizontal flow coefficient decreases as K of the filter media increases. However, it is found that for a given surface area of the soak-away rain garden, K of in-situ, and K of filter media, the horizontal flow coefficient increases as depth to groundwater table increases.

Multiple Regression Model of a Soak-Away Rain Garden in Singapore

Under the possible hydrological conditions, with a design hyetograph of 3-month average rainfall intensities of Singapore, multiple regression equations on hydrological processes, specifically on overflow volume, average vertical ex-filtration rate and horizontal flow coefficient, of a soak-away rain garden are established based on simulated results of a mathematical model. The model that is based on Richard’s equation is developed using COMSOL Multiphysics. The regression equation on overflow volume and the regression equation on log of horizontal flow coefficient show a very strong relationship with the independent variables (saturated hydraulic conductivity of the filter media, saturated hydraulic conductivity of the in-situ soil, depth to groundwater table, and surface area of the soak-away rain garden). The coefficients of determination of the fitted equations on overflow volume and log of horizontal flow coefficient were 0.992 and 0.986, respectively. However, the regression equation on average vertical ex-filtration rate has high p-values (p-values > significance level, α = 0.01) for saturated hydraulic conductivity of the in-situ soil and surface area of the soak-away rain garden. Thus, forward stepwise regression was used to develop the best regression equation on average vertical ex-filtration rate with saturated hydraulic conductivity of the filter media and depth to groundwater table. The coefficient of determination of the fitted equation was found to be 0.911. These easy to use regression equations will be of great utility for local mangers in the design of soak-away rain gardens.

Easy-to-Use Look-Up Hydrologic Design Charts of a Soak-Away Rain Garden in Singapore

As catchments become urbanized due to population growth the impervious surfaces created by buildings and pavements in the expense of permeable soil, depressions, and vegetation cause rainwater to flow rapidly over the landscape. To mitigate the adverse impact of urbanization such as increased flooding and depleted groundwater recharge, around the world, several best management practices, in other words, green infrastructures have been practised, and soak-away rain garden is one of them. However, to have a rapid assessment of soak-away rain gardens on a range of potential hydrologic conditions (e.g., size of the soak-away rain garden, saturated hydraulic conductivity of the in-situ soil, and saturated hydraulic conductivity of the filter media), hydrologic design guidelines or design charts of soak-away rain gardens that are specific for local conditions are not currently available for many regions including Singapore. Thus, in this paper, with a design hyetograph of 3-month average rainfall intensities of Singapore, hydrologic design charts, especially, design charts on overflow volume (as a % of total runoff volume) of soak-away rain gardens are established for a range of potential hydrologic conditions by developing a mathematical model based on Richard’s equation using COMSOL Multiphysics, a finite element analysis and solver software package for various physics and engineering applications. These easy-to-use look-up hydrologic design charts will be of great utility for local managers in the design of soak-away rain gardens.

An Interface to Model 3D Hydrological Process of a Soak-Away Rain Garden

To mitigate the adverse impact of urbanization around the world, several best management practices, in other words green infrastructures, have been used in a way that protect the natural hydrology of the catchment and are more beneficial to the environment. Soak-away rain garden, shallow, landscaped depressions commonly located in parking lots or within small pockets in residential areas, is one of those best management practices or green infrastructures. However, though in the past few decades the mathematical modeling work and the science of computer simulation have enhanced the understanding of hydrological processes, there is still a lack of modeling studies that focus on understanding the three-dimensional (3D) hydrological processes, such as the 3D ex-filtration process of a soak-away rain garden in a sufficient level of details. Thus, this paper develops a 3D mathematical model to represent the hydrological processes of a soak-away rain garden using COMSOL Multiphysics Java API, a Java-based interface of COMSOL Multiphysics. The developed model is demonstrated with a design hyetograph of 3-month average rainfall intensities of Singapore.